question_answer

The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an angle of \[60{}^\circ \] with the horizontal, then the length of the wire is                                                              [SSC (CGL) 2013]

A) \[8\sqrt{3}\,m\] 

B) 8 m

C) \[6\sqrt{3}\,m\] 

D) 6m

Correct Answer: A

Solution :

Let the length of the wire be \[l.\]

In \[\Delta ADE,\] \[\sin 60{}^\circ =\frac{DE}{AD}\]

[AD = length of wire]

In \[\Delta ADE,\]\[\sin 60{}^\circ =\frac{DE}{AD}\]

\[\Rightarrow \]   \[\frac{\sqrt{3}}{2}=\frac{36-24}{l}\]

\[\Rightarrow \]   \[l=\frac{12}{\sqrt{3}}\times 2\]

\[\therefore \]      \[l=\frac{24}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=8\sqrt{3}\,m\]